On the projections of Laplacians under Riemannian submersions - Huiling Le (International Journal of Mathematics and Mathematical Sciences)
We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace-Beltrami operator on M. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.